As it's an upstairs (I presume) radiator you need to make sure that the heating is actually pumping water around at the time you bleed the rad - make sure the boiler is on and turn the thermostat up to "tropical" just for the few minutes you need.
If you don't do this it's quite possible to bleed air *into* the sytem rather than out ...
I'm having the same problem with my lounge radiator, the bedroom one won't come on at all. Neither need bleeding as that was the first thing I tried and water came out of both immediately.
I agree, that's the theory Hoppy - but not all systems have headers, and even mine (which does) has one tall bathroom rad which seems to need the pump pressure before it will bleed properly.